The work done by a force $\vec F = (-6x^3 \hat i) \text{ N}$,in displacing a particle from $x = 4 \text{ m}$ to $x = -2 \text{ m}$ is .............. $J$.

If the roots of $x^3-42 x^2+336 x-512=0$ are in increasing geometric progression,then its common ratio is (in $: 1$)

Equimolar solutions of the following were prepared in water separately. Which one of the solutions will record the highest $pH$?

For $0 < x \leq \pi$,$\sinh ^{-1}(\cot x)$ is equal to

$AB_{3(g)}$ dissociates as $AB_{3(g)} \rightleftharpoons AB_{2(g)} + \frac{1}{2}B_{2(g)}$. When the initial pressure of $AB_3$ is $800 \ torr$ and the total pressure at equilibrium is $900 \ torr$,what fraction of $AB_{3(g)}$ is dissociated (in $\%$)?

On increasing the reverse bias to a large value in a $PN-$junction diode,current